“The family is back home and are overjoyed with the new addition,” says Bublé’s rep, also sharing that the couple chose Amber for the 42-year-old Canadian singer’s mother and Betty for Lopilato’s mother.

Lopilato, 31, announced Vida’s arrival on Instagram Thursday, sharing a black-and-white photo of her newborn’s tiny hand and hinting at her name in the caption.

“How to explain that our heart explodes with love? That there’s not enough hours in a day to think about it. I thank God for making us this gift of life and happiness! Because looking in her eyes is looking at heaven itself!” the Argentine actress wrote, in Spanish.

“We love you to infinity and beyond. We waited for you notonly to grow as a family… you gave us light, hope, you are and will be our souls’ life,” she added, writing “Vida” for “life,” with a capital V.